Daily demand for a certain product is normally distributed with a mean of 100 and a standard deviation of 15. The supplier is reliable and maintains a constant lead time of 5 days. The cost of placing an order is $10, and the cost of holding inventory is $0.50/unit per year. The company has a goal of not stocking out 90% of the order cycles. Assume that sales occur over 360 days each year.
a) Calculate the optimal order quantity for the item.
b) Assuming that the item is reviewed every day, calculate the required safety stock for the item given the 5-day supplier lead time.
c) How much inventory would the company have on average?
d) How many weeks of supply?